"Weight" can be used as a noun or a verb. As a verb, adding "s", you shall know why?
As a noun, let me give you a few examples:
Please indicate height and weight on the form.
My weight is 150 pounds.
The boat is sunk by the weight of the cargo.
I stay in good shape by lifting weights.
I use pie weights while baking to keep pie crust from bubbling.
His recovery has lifted weights of my mind.
Therefore, to add or not to add "s" really depends upon the context.